Planooraph co



J. BECKER, DECD. E. BECKER. ADMINISTRATOR.

ART OF CUTTING SCREW THREADS.

APPLICATION FILED FEB. 1. 1918.

1 3 1 8,045 Patenwd Oct. 7, 1919.

5 HEETSFSHEET 2.

At 61F At 32F 6 Error Change gear 1 M d M '4' d 1. .2. 2 f" I Foi'muld.

. M M per I F; n,

- million M inches millimtars Lodge 13 330 +00. 1-000 606 606 3 3';'"-

6 +o-2. 1-00z0 7.0 +9. 95 7 4 9 s Becker 3 10 0- 1 3 1 3 o .Boys 63 chambers 4 8 1 1125+ o-z 1-000 013 18 -16 2 7 51 Wead' 5 127+0-0 1-000 000 0 183 5! 5. YV/izfnes Inventor rmml mun ANIIIUIAPII 00., WAsllmuToN, n c.

1. BECKER, M00.

5- BECKEII. ADMINISTRATOR.

, ART OF CUI'IING SCREW THREADS.

I APPLICATION FILED I'EBII. I9l8. 1 7 1,318,045, Patented Oct. 7,1919.

l. BECKER, DECD.

E. BECKER. ADMINISTRATOR- ART OF CUTTING SCREW THREADS.

APPLICATION FILED FEB.I.I9I8.

1,318,045. 1 L Patented Oct. 7,1919.

5 SHEETS-SHEET 5.

TH BL E FOR CONVERT/N6 11v nccakomvcs WITH EQUATION 2. 43, mares -.'1o z r n) STEEL mcnzs' & STEEL MILL/METERS &

= v 6-136 047 1 o 1 5B 1 395 Witness 8 Inventor- 'rns COLUMBIA PLANOGRAFH cn.. WASHINGTON. n. C

30 tained by using..inthe set 'of change wheels Jaeeswa we Wi wam-mew COLUMBIA; Bis-seas emv l v eeeseee eaqs s eeeeeew e eeester -ewe s eevea es swee em sesl ai ntee ct it 1 5 9.

conti uation of-app1ication' -Ser ia1 No.-16 8,446, ii1eg1 May 14,1917. This appli cation ni a ifebi uar 7,1918. Ij serial li'o.215,843;

To all whom it may concern.

Be it known that I JOSEPH.BEQI ER,acitizen of the 'United States, residing at-: 1315 :Fairmontv street N. W.,- Washington, *District of Columbia, U. S. -A., have' invented a new and usefullmpro-vement in the Art of Cutting S crew -'l?hreads,xofwhich the :following is a specification. r r i The present patent application, identified as Case -Ay, is a: continuation of prior herein merged and therefore, hereby abandoned Gase Aw, -erial No.- 168,41 6, filed May 1 1, 1917, which was allowed-August 7, 1917. This present Oase Ay, like -itsherein merged predecessor, Case Aw, is based'ion a further and somewhat -difl'erent development oftZhe inventive.idea-involved in the combined inchand mil-limeter endmeasr uary' 27 ,1 1917 as a continuation of my there ure of my prior patent application, Gase Av, Serial No. 1%,903, whichwas filed-Janinrmerged earlier application, Oase-Q, 1 Serial No. 562,181, itself filed May 185 -1910.:

The present inventionrelates to the art of cutting screw threadsIj itsi-prir'ne object" being to 'permlt of cutting--thre'ads having 1 a millimetric pitch, by means of a. lathe whose -'leacl screw'fis based on the English inch.

The object inview has heretofore been at- My present invention ,based ongthe ,di scov'ery that a translating gear wheel having not more than fortyjthree teeth permits of securing a more accurate resul-tpbesides having the obvious advantage o f being much less.- expensive and JessBcumhersome. {Ehe 12,7 tooth wheel is iir fact ,HlllCll-flflIQfilly. and, therefore,; also much .more ;.expensive, than anyavheelin commonusegi In my said prior application,-:GasezAvfltis made plain that ,the ,usej.of.zthe 127 stOoth wheel is really based on the assumption that p 5 .inches :127 millimeters (1) also that such equation holds only under special conditions, as, ,forinstance, whenthe metric scale and the inch scale are both graduatedon the same bar, andso as to beexact at or about the same standard temp erature'.

As the U. S. and English lathes are intendedto be standard at 62 degrees Fahrenheit, it follows that any millimetric pitch cut in such lathes, with theaidof atranslating wheel having 127 teeth, can only be exact at or: ab out 62- degrees Fahrenheit.

#The standard temperature ofmetric' gages,

however, is 32 -degrees' Fahrenheiu or '30 degrees Fahrenheit lower than 62, andthis reductionzintemperature is sufficient to produce an appreciable contraction which must be. allowed form the change wheels because all ,gages, lathes, JetcL, being madeof steel or iron, expand approximately 11 in a million :per degree centigrade and a difference of 30 degrees. Fahrenheit being equal to 50/3 degrees centigrade produces an expansion 'bf11X50/3 equal to"5 50/3 or 183 V and 1 parts in a million,

theprime number ,is the largest prime number involved inequatio'n 2, and it is the oi ilyonewhich callsffor the useof a special or .translating wheel of 43 teeth, in-

stead of the usual wheel 619127 teeth.

' Special "wheels having tooth numbers of twice 43,0r 86, and" three times 4:3, for 129,

ma resent .advanta es' in certain cases' I 7 and air-additional special wheel of Thy 13 or 91 teeth also has its advantages. lithe accompanying drawings:

Figur es 1' 'a1'id" ,2 diagrams showing -hdw" a] steel bar A, 1092 millimeters long,

and ,a steel'bar B, 43 inches long, will, when "kept at "their respective standard temperaturesoif 32 and 62 degrees Fahrenheit," as in Fig. 1, differ-in 'l'en'gth byian amount cl,

which vanishes whenever the said bars A are broughtto one same temperature, asinFig.

vFig. 3 is a dlagraml of the simplest arrangement that'can be used ,in accordance with'my invention for cutting, 111 a steel rod W, a rnetric thread, whos'e pitch 7) at 32 F."- is 3 millimeters; by means of the tool T having a lead-screw L, whose pitch P at 62 F. -i *-1/1-inch;sucharrangement requiring two special wheels, to wit: audriver preferred number of teeth.

Now, let the temperature of bar A in Fig. 1 be raised 30 degrees from 32 F. up to 62 F., and it will expand to become, as in Fig. 2, equal to bar B, because its expansion.

.of the lead-screw be 1? equal 1/n inch (71 Referring to Fig. 3, let it be required to Fig. 4 is a diagram of an arrangement (being, as explained above, 183 and 1/3 40 comprising two driver wheels a, Z) and two parts per million, or 550/3000000) will be driven wheels at, b, to form a combination 1092 550/3000000 or 0.2002 mm., which is that cuts the same thread as in Fig. 3 from substantially the same as the difference d of the same lead-screw; the main object of this 2/10 mm. shown in Fig. 1. combination being, to permit of using the The bars A and B being, therefore, equal current wheel sizes of 36, 42, and 78 teeth, in length when both are kept, as in Fig. 2, instead of the special wheel of 91 teeth that at 62 F., they will henceforth expand and is necessary in Fig. 3. contract together, so as to remain equal in Figs. 5 to 7 are charts which are useful length at all temperatures. in explaining the exact nature and scope of Assuming that no out in a lathe is made my present invention. sufliciently heavy and fast to heat the work Fig. 8 is a table which permits of conappreciably, the lathe, its lead-screw and the verting, by means of simple additions, any work, may all three be considered as being either -Whole or decimal number of inches sinmltaneously at the same uniform though in the lead-screw, to millimeters in the cut variable temperature. I thread, or vice versa. 1 If, therefore, at any given moment and The principle evolved in equation 2, above, temperature the nominally 1092 millimeter is illustrated in Figs. 1 and 2, showing two steel bar A represents a piece of work in a steel bars distinguished as Bar A and .Bar' lathe, the nominally 43-inch steel bar B will, B. Bar A in Fig. l is supposed to be kept at at the same given moment and temperature, the standard temperature of metric gages, represent the correspondingly equal part of 32,F.,while barBis being kept at the higher the lead-screw in the same lathe. The true standard temperature of inch gages, 62 F.; equivalent for cutting steel or iron screws and under these conditions bar A is, as inis, therefore, the equivalent defined by equadicated in the figure, exactly 1092 millimetion 2, above, and illustrated in Figs. 1 65 ters long, Whereas bar B is exactly 43 inches and 2. i V long; and their difference d is equal to two- The rule for calculating a train of change tenths ofa millimeter, because 43 inches at wheels to secure any desired pitch, or feed 62 F. equal 254 times 43, 01' 1092.2 mm. per turn of work, is given by the general at 32 F. equation:

a.b.c.d feed 10 of tool per turn of work W a.b.c.d -feed P of tool per turn of lead-screw L (3) Here a b, 0, (Z, are the respective tooth numing the number of turns per inch in the lead- .bers 0 wheels whose teeth act as pushing screw), then equation 3 becomes: or driving teeth; while a, b, 0, (Z, are the b d 2) millimeters respective tooth numbers of wheels whose m=m teeth act as push-receiving or driven teeth. t

The number of driver wheels used rarely :W (5) exceeds. three, but four are given in equa- 11nch tion 3 so as to cover the most complicated b 111 Vie f cquatlon 2, one mch 1s caseg 1092/43 millimeters, hence Single Wheel idlers, such as m in Fig. 3, abcd 432m 43 m being used for the sole purpose of filling air m m m (6) gaps and reversntg the dlrefltlon of roitatlom where 32 may be any desired millimetric pitch may be of any and me, l i to be cut in the work W; and it may be any z z' i i l desired number oflead-screw turns per inch. P an 1 0 86 611615 equadon For cutting millimetric threads two 3, firstas a drl ven wheel of 02 teeth, then drivers, a, b, and o driven Wheels as dnveir of a] eqtml teeth; so'that the are generally suiiicient, and in sonfe cases 'mtlo equzllls unity 1 5 dloes i f these are reduced to one driver wheel a and the result as f t we 0t er one driven wheel a, with the usual idler a: tors a, or a a b 0 2 d to connect them Equation 15 general and The manner of using this fundamental .cludes Ellery kmd of Wheel that may be used equation 6 will now be illustrated by a few in a train of change wheels. selected Sim 316 6mm 318? If the linear feed per turn of the work be l L 1 79 millimeters; and the linear feed per turn Example 0716' use a'train of change gears comprisinga single driver Wheel a, and, therefore, asingle driven wheel a, to cut, in a -rod W, a metric thread of pitch 2? equal 3 millimeters, from a lead-screw L Whose threadmakesn equal 4 turns per inch.

Equation 6, above, yields directly showing that the driver wheel a should have 43 teeth, and that the driven Wheel a should have 91 teeth-" The idler m, of course, may have any preferred number of teeth."

Example two. 1 Referring to Fig. 4, let it be required to use a train of change gears comprising two driver Wheels a, hand; therefore, also tWo driven heels a,-b", to cut, in a rod W, a

metric thread of pitch p equal 3 millimeters,

from a lead-screw L Whose thread makes 9?. equal 4 turns per inch. "This is the same problem as in Example one, excepting that two driver Wheels are used insteadof one.

Equation 6, above, yields directly as beforein Exampleone; 1

Assuming that We have a series of change Wheels, Whose tooth numbers are multiples A lathe having a lead-screw whose thread makes n equal 12 turns per inch, and having a set of change Wheels vvhose tooth numbers are multiples of 4, is to. be used. in cutting the fifteen difi'erentpitches of the Systme International, .Which is.v referred to more fully in Note 13 belowa;

Equation 6, above, yields in the present case: 1

and as we must, in the present example, use

tooth numbers that are multiples of 4, We may Write That is to say, any one of the fifteen different pitches of the Systeme International may be cut as indicated in the annexed Table A, by using only three dilferent Wheels of 28, 43 and 52 teeth, in combination with one single variable change Wheel having 6 or 16 teeth.

Table A.

Lead-screw turns, n= 12. Variable gear wheel, b=16p.

p a l a b b 2.5 40 3 mm. 48 3.5 56 4 mm. 64 4.5 72 5 mm; 80 5.5 88 6 mm. 96 6.5 104 7 mm. 112

Emample four.

A lathe having a lead-screw Whose thread makes 71 equal 8 turns per inch, andhaving a set of change wheels Whose tooth numbers are multiples of 5 is to be used in cutting the fifteen different pitches of the Systemc International. The set of change Wheel comprises, furthermore, two special Wheels for cutting metric threads, one of twice 43 or 86 teeth, and one of 7 byl3 or 91 teeth, and it is desired to use these Wheels instead of a Wheelof 43 teeth.

In the present case, Equation 6 above yields: 1

a1) 43.p.8 43.p.2 a.b" 7.12.13 7.3.13

whence a.b l .3

That is to say, all metric pitches of the Systeme International may be cut, asindicated in the annexed Table B, by using only three difl'erent Wheels of S6, 91, and 60 teeth,

in combination with a sin le variable change wheei Whose-variable toot number 5 is 20;).

Table B.

Lead-screw turns, a= 8. Variable gear whee], 11:20

p a a b b 1 mm. 86 91 60 1.25 1.5 1.75 v

2.5 50 3 mm. 6O 3.5 4 mm.

1 5 4.5 90 5 mm. 100 5.5 110 6 mm. 120 6.5 130 7 mm. '140 In using any one of the combinations in Table A, or in Table B, it is wellto note that special circmnstances may impose changes in the arrangement of the wheels, or may 25 impose substitution of wheels having other tooth numbers, or the insertion of an idler wheel. All such permissible changes are controlled by the following general rules,

which, so far as I know, are here-clearly and 30 fully enunciated for the first time:

RULE 1.Transposing any two driver wheels (such as a and b in Fig. 4 does not changethe pitch [9.

RULE 2.Transposing any two driven 35 wheels (such as a and 'b in Fig. 4) does not change the pitch p.

RULE 3. If the tooth number of any one driver wheel, and the tooth number of any one driven Wheel (such asnumbers a and b 40 in Fig, 4) both'be multiplied, or else divided,

by the same number, either whole or fractional, no' chafnge is mad'e in the pitch 7).

Ruin; 4.Th'e thread cut is left handed where thenum ber of wheel-contacts is odd ('asi-t*would be in Fig.3,'if no intermediate idler "wheel 'wereused) RULE 5.---'1 he =thread "cut is right-handed where the number of wheel-contacts iseven (as in either Fig. 8 or Fig. 4, where the number of wheel-contacts is two).

The only restriction placed "on Rule 3 is that the final iresult must contain whole number tooth numbers, exclusively.

It was pointed out above that a single wheel idler of m teeth-is the equivalent of a compound idler comprising two equal wheels, to wit: adriven wheel of m teeth and a driver wheel of 0?, equal w, teeth; also that such single wheel idler may have any 0 other arbitrarynumber of teeth. This principle, that'a single wheel idler may have any number of teeth, was quite evident where first referred to, but it is well to note here, that it'is in accordance, and substantially "*Ifeidentical, with the present Rule 3, Whose utility is further illustrated by the following example: 11 Y i Example five.

A'l-a'the having a leadscrew whose thread makes n equal 12 tur'ns per inch is'to be used to cut the fifteendifl erent pitches of the Systeme International by meansof a set of change wheels comprising my two special wheels of 86'and 91lteeth,Iwith all other tooth numbers running as multiples of 6, from 24 to 96, including a single duplicate gear wheel of 48 teeth.

Equation 6, in this case, yields: 7

at 48. p.1 2 43.p 80

whence i861? (fly Ti or finally 4 a1) ee-24p 57179148 and this, by transportation under Rule 1, is equivalent to y a.b' 2a .s6 f

That is to say, the fifteen different pitches of the Systems International may be out with a four-wheel train such asseenin Fig. 4, but whose respective tooth numbers are Here the wheels 91 and- 86 constitute an invariable compound idler cf 6, Fig. 4-, havone of its elements I) or 86 in constant engagement with an invariable lead-screw wheel I), of 48 teeth and having its other idler element a of '91 teeth swung up intoengagement with the driver a which constitutes the single variable element of the combination. The-tooth number 24p. of this 1 10 variable wheel a increases regularly from 24 to 168, as indicatedin the annexed Table C:

Table 0.

Lead-screw tums, n=12. Variable gear wheel, a= 12p.

a. a b b I The 86/91 compound idler;

Whenever the 86/91 compound idler is used as in my aid Tables C and C, equation 6 may be written as where the second member and the last, by

cancellation, yield a p.'n. b 24 7 Hence, if the pitch 3) to be cut is 241 milli meters, and the pitch of the lead-screw is the even, but approximately equal, length of one inch, this last equatlon becomes whence If, therefore, an inch standard lathe has a a full set of change wheels @for cutting t, t, 25", etc., turns to the inch, with the aid of a single Wheel idler; then, the simple substitution of my 86/91 compound idler, for such single wheel idler, does convert the lathe into a metric lathe which will cut the same 6, t, t', etc., series of turns in an exact metric length of 24 millimeters. Moreover, this length of 24: mm. differs so little from an inch that the cutting range of the lathe is not changed in any marked degree.

My 86/91 compound idler, therefore, simply serves as a substitute for the usual single wheel idler, to convert, in the most direct manner possible, any inch-standard lathe, into a metric lathe.

The three different inches.

From disclosures in my said Case Av, it appears: first, that the legal value of the international meter in the United States is 39.37 United States legal inches, secondly, that the legal value of the same international meter in Great Britain is 39.370113 British legal inches.

These two values may be expressed in the form of equations, as follows:

1000 mm.:39.37 U. S. legal ins (7) 1000 mm.:39.370113 Br. legal ins (8) Multiplying each of these equations throughout by 127/1000 produces 12? 1nm.:4l.99999 U. S. legal ins "(9) 127 mm.:5.000004351 Br. legal ins (10) which are both complete and exact values because all decimals given in the two legal values have been retained in the calculation. Equations 9 and 10 may evidently be rewritten in the form 127 =5 1W) legal 11151....v (11) 127 mm. =5 1 BI'- and these two equations divided throughout by 5 yield 2 25.4 mm.=(1- )ll 8. leg. 1I1S (13) V 0.87021 25.4 II1HL= 1 'bm) BI'- 16g,- 111 (14) In my said Case Av I have moreover given the name metric inch to the length defined by the exact equations, to wit:

127 mm.:5 metric inches (15) 25. 1 mm.:1 metric inch (15) 'This metric inch, by equation 13,- is 2 parts in a million shorter than the ill. S. legal inch, and, by equation 14, it is less than one millionth longer than the British legal inch.

The metric inch of exactly 25. 1 mm, therefore, is a very convenient, intermediate or compromise inch, difiering less from either one of the two legal inchesthan they difler from each other; and it is the only one used in the present specification, wherever the French and the English lengths to be oomparedarc supposed to be lrept, as in Fig, 1, at their -respectivestandard temperatures of 32 and 62 degrees Fahrenheit, Under the special; conditions of Fig. 1, therefore, the millimetric equivalent of. a given number.- I of inches is I inches: (1X25J1) n1m (16) so that bar 13, in 'Fig. 1, being 43 inches long at 62 R, must, aspreviously noted, be equal to -13 25.-l-, Or 10922 nillinieters inbar. A, kept at 32 F.

Notes on ThermaZEwpension.

No'rn 1.-Accordingto Le Chatelier (Complies Rcndus ofthe French Academy of Sciences, Paris, 1889, tome. 129," page 332, lines 19 to 25), it may be admittedthat the different varieties ofi'ron and steel, at ordinary temperatures, exp and eleven .partsper million per degree centigrade.

NOTE. 2.Commandant I'I-artmann, of the French artillery, with his.autom;atio re v cording comp arator fomid theexpansion of ordinaryv steel to be 10.7 parts per, million per degree centigrade. See Uomp tes Rcmius of the French Academy of .S cien ces, Paris, 1895, tome 120, page 1027, foot note.

No'rn 3.Kaye (of the National Physical Laboratory, I England) and ,Laby, in their Tables of Bin sierr and Ohemioal 0072-. stcmzfs, London, 1916, page 53, for the expansion of iron .in its differentforn s give:

Expansion in millionths. per 1 0.

Cast iron 10. 2 Stee1.-.... 10.5 Do. 11.6 Wrought iron. 11. 9

Sum 44. 2 Average. 11. 05

NOTE L-The "Landolt-BornsteinPhys; kaZisch-Uhemische TabeZZcmf edited under the auspices of the Prussian -Aca-de1ny of) Sciences, by Bernstein and Roth, Berlin,

give values which I have re-exprcssed, and re-arranged in size order, as follows Norn,5.-The Smithsonian Phi steal Ta,-

bZesj. fiftlrrevised edition, prepared .by F.

Expansion Condition. in millionths per l" 0.

0 to 300 C. 9.307 0 130025 0. 10.2 7 0 to 80 0. 10.563 F 15 to 36 0. 10. 95 16 to 36 C. 11.10 0 to 750 C. 11.391 7 0 to 750 0. 11.087 0 to 500 C. 11:915

F. Fow1e,lVashington,- D. (3., 1910, page 222, Table 219, for the thermalexpansion of iron in its diflerent forms, give values which I have re-expressed and rearranged in size order, as follows Expansion Condition. in millionths per 1 C.

Cast iron. 191 to 16 8.50 0. 40 10. 01 Annealed st 40 10. 95 Wrought iron 18 to 100 11.40 Soft iron," 40 12.10 Steel. 40 13. 22

66.78 Average 11. 13

tooth-driven wheel of Note 20, below, could only be exact in case the expansion per degree. centigrade for. all materials involved were equal to zero. The- Boys (iii-tooth driver wheel of NQLQQ23, below, accidentally provides for an insufiicient expansion of 0.2/ 1600 multiplied by 3/50, or 7,5 mi-llionths per degree centigrade; while the Lodge 13- inch solution of Note 21, below, accidentally provides for a highly excessiveexpansion of 0.2/330nnultipli'ed 'by 3/50, or 36.35 millionths per degree centigr'a-de; but each of these allowances was involuntary and, to their authors, apparently unavoidable, hence they were as stated, purely accidental, and neitherone comeswithin the comparatively narrow range from 8 to 14: millionths, which according to Notes 1 to 5, above, surely comprisesall values of the thermal expansion of iron inits most diversified forms and conditions of use.

Notes on standard temperatwes.

Norn 7. ,Th e-stan dard temperature of the international meter is 0 centigrade 0r 32 F., this being the. temperature of the bar when it is'surrounded by a mass of shaved and melting ice, which constitutes the most convenient,cert;ain and reliable thermostat known to science.

No'rn 8.As a result, there never have been any doubts as to'the temperature, 32 F of the standard meter of 1799; such as have frequently arisen,-in the past, with reference to the standard temperature, 62 F., and,; therefore, also witlnreference to the .1 length, of the original imperial standard yard of 1855 (which; however, had the additional objection of being made of a copper alloy, which, according to page 41 of the Kaye and Baby tables (fully-cited in Note'3, above), is now known notto be suitable for standards of length. i i a N orn 9.Metric gages, therefore, for all scientific purposes are made standard at this same temperature 0 C. or 32 F.;-but, for industrial purposes,lcer tain, and especially German, makers had adopted a standard temperature of 15 C. or 59 F. According to Guillaume, however, the French artillery (section technique de lartillerie), in or about 1895, made a thorough investigation of the whole question, and they arrived at the conclusion that the introduction of any such secondary temperature, for industrially used gages, would be a useless and troublesome complication. They accordingly adopted for the purposes of the French artlllery the same standard temperature, to wit: 0 C. or 32 F., as that used for the original meter barsof 1779 and 1889; and the same practice is followed by the International Bureau, the French Navy, the well known Parisian house of Bariquand & Marre, the universally celebrated Socit Genevoise, of Switzerland, and also, where the measure is metric, in the wonderfully accurate J ohansson gages. Moreover, the practice has met with the indorsement of the International Committee, which has frequently discussed, and condemned, the use of any secondary standard temperature. (See Comit International des Poids et Mesures, Proces-Verbaua' des Seances, as follows: session'of 1901, pp. 125126, and pp. 137-11; session of 1909, pp.- 111l13, and pp. 145-150; also the very complete article on. Industrial standards oflength, by Guillaume, of the International Bureau,in La Nature, Paris, July 30, 1910, pp. 130-135, particularly 133.) p Norn 10. According to Stadthagen, of

the Normal-Eichungskommission, measures of length arevoificially tested and verified in Germany for the normal standard temperature of 0 G; unless the particular gage or rule submitted for verification is one that is expressly intended to be exact at a different temperature, and hasthis different temperature distinctly marked thereon.

(See Zeitschriftdes Vereines De'utscher 1ngenz'eure, Berlin, September 9, 1911, second half 'of vol. 55, p. 1529, column2; particularly the footnote 'inlines-SO to 63.) V

NOTE'II.NO man everwill know exactly what62 F. meant in 1855, because the corrections to be applied to thethen exclusively used mercury in glass thermometers were not fullyunderstood. The present British legalized ratio of the yard to the meter,

however, as fixed in 1895, by coiiperation of the London Standards Office with the Bureau International, near Paris, now makes 62 F. equal to 16.667 C. of the 1887 standard hydrogen thermometer of the International Committee, and this equals 16.742 C. of the mercury in verre dur thermometer whose irregularities are now thoroughly understood. (See lines 10 to 31, page 18, of the 25-page report of Benoit, entitled De'terminat-z'on (Zu Rapport clu Yard au Metre, which is the first one of the six separately paged scientific papers constitut- General remarks.

NOTE 12.In all that precedes it is assumed that the work 1V in Figs. 3 and 1 is of iron or steel. To consider it as being brass, or any other different metal, would needlessly complicate matters by introducing differences in the coeflicient of expansion that may be, and that are, wholly ignored in practice. 7 r

N OTE 13.The Systems International of screw threads is the metric standard corresponding to the well known English standard of \Vhitworth, and to the American standard of Sellers. It is frequently, but incorrectly, referred to as the S. J. system because its abbreviationS. I. is printed S. J. in Germany, where they stubbornly insist on using the same character J for the two letters I and J. One of the most complete and authoritative accounts of the S. 1., or international system of screw threads, is found on pages ear to 457 of the Bulletin cZe Za S0- ez'e't cZEneouragemenzf pour Zlndustrie NationaZe, Paris, 1899, which gives on page 451 the fifteen different pitches listed in my annexed tables A, B, and C. These same pitches are listed in any reasonably complete modern pocket book for mechanical engineers. See, for instance, The Mechanical Engineers Reference Book of Henry Harrison Suplee, Philadelphia, 1913, page 318. Suplee calls it internationals (with a final e), but this is another frequently com mitted error which must be due to one of the earlier, and surely not French, writers on the subject.

Norn 14.Consider W, in either Fig. 3 or Fig. 4, as a lead-screw and L as the work, reversing tool T to correspond, and you have the inverted picture of a French lathe cutting quarter-inch threads, from a leadscrew having a pitch of 3 millimeters.

NOTE 15.I am aware that structures which are supposed to be c. pable of cutting metric threads from an inch standard leadof Putnam, also alleges that the Putnam device is adapted to cut metric threads from an inch lead-screw, but the book does not anywhere make the slightest reference to the number of teeth that might be used to secure such result.

NOTE 17.-I am aware that several authorities, Shaw cited below, for instance, recommend, as being sufiiciently accurate, the use of a wheel of 63 teeth, their calculations being virtually founded on the as sumed, though not explicity stated. equiva lent of 63 inches equal to 1600 millimeters. But, according to the conversion tables given on pages 5 and 10 of the Smithsonian Physical Tables (prepared by Frederick E. Fowle, and published by the Smithsonian Institute, WVashington, D. C., 1914), 63 inches must equal either 1600.1986 mm. or 1600.203 mm, according to whether the inches used are British inches of U. S. inches; and either of these values, to two decimal places, equals 1600.20 mm. This twotenth millimeter excess, in the light of. present disclosures, may be treated as representing athermal expansion whose relative value is 2/16000, or 125 parts in a million, instead of 183 parts in a million, as provided by my rule. The 63-tooth wheel, therefore, instead of being less accurate for present purposes than the 127-tooth wheel, as universally understood (see, for instance, Thomas, R. Shaw, Lathes, Screw M ctchines, Boring and TlMnlILg Mills, l\ lanchester, England, 1903, pages 177 to 17 9.), i in fact more accurate.

No'rn 18.Very full tables of change wheel trains adapted to cut metric pitches, with a 63.-t0oth wheel from a lead-screw having either 1 2 or 1/4e-inch pitch are given in Chapter X, pages 133 to 149, of Screws and Screw M (thing with a Chapter on the Milling Machine, edited for and published by the Britannia Company, makers of engineers tools, Colchester, England, 1891 (copy in the Patent Office Library),

No'rn 19.Any rule for cutting metric threads from an inch standard lead-screw may, in the light of present disclosures, be considered as based on the more or less directly made assumption that a certain whole number, I, of inches is exactly equal to a certain corresponding whole number, M, of

'& 1,318,045

5 inches; 127' mm (17') 1'3inehes; 330 mm (18) 43inehes= 1092mm (19) 6,3 inches: 1600 mm (20) 43s inehes 11125- m ('21 Thatis h ays if ny s re Whale um f n hes be assume equal o. c r spen i g whe n mben 0 mil im er then my" iiiimlemea a equatien 6. abo ay be W e i the gene ized. ter e wit- NOTE 20-.-Equati,on 17; is implied in the proposition of Charles K. Weed, first made in the American Journal of Seience (tncl Arts, New Haven, Connecticut, 1882, third series, vol. 23, pages 17 6 and 177'; and again made, by the same author, in the London, Edinburgh, ancl'Duhlin Philosophical M agazine anclJom'nal ofiSciencWfor June, 1883, fifthseries, Vol. XV, pages .43-8-and 139. In accordance with my" equation 22 above, equation 17" leads to the following change gear formula, to Wit:

and, as 127 is a prime number, this involves the use. of a driven wheel having 127 teeth. This so-called: translating Wheel is very generally known, as proved by communications from 12 d-ifierent S. and foreign manufacturers-andengineers, collected in M achinei y New York, February, 1900, pages164, 165. For a very full exposition of its use, see:v Erik Oberg, Handbook of 8777816 Tools, New York, 1908, Pages 58 to. i Y

NOTE ,21.-.Eq uation 18. is. given in the form: 13. inches equal 33. centimeters. by Sir Oliver Lodge, in -Natune, London, March 19, 1891, vol. 413', page 4163, column v2, middle five-line paragraph and it is implied in the virtually identical relation, 6.5 inches equal 16.5. centimeters, of DeJV-ries, The Calculation 0; .Ohange Wheels for 'Scnew Getting on Lathes, London and New York, 1914, page. 23 and page 27. (Copy in the Scientific Library of the S. Patent Oflice.) The change. gear torinula corresponding to this equation 18. is;

rib-.041 13.10.n 6"Ib.jc";.2l," 7"380,. ow -.lf q at .0n .19 is the one di covered and first disclosed by me in the P e n app wt n,v Av, wh h n only makes a valuable contribution to the art, but, furthermore, sheds, it is believed,

considerable light on the work of all pre vious investigators 1n this l1ne. The change gear formula corresponding to this equatlon 19 is evidently that of equation 6 above, or a.b.c.d 43.p.n

NoTE 23.-Equation 20 is implied, first in the change wheel trains disclosed by C. V. Boys, of the Royal College of Science, in Nature, London, March 12, 1891, page 439; secondly, in the Britannia tables of Note 18, above; thirdly, in the Shaw citation of Note 17, above;fourthly, in the 315-inch equivalent of Ernest Pull cited at length in Note 25 below. The change gear formula corresponding to this equation 20 is:

NOTE 24.Equation 21'is iinpliedin the which is based on myequation 22 above, and

out by 5, assumes theform: 63 inches equal 1600 millimeters; as in equation 20, above. NOTE -26.D. de Vries, in The Calculation of Change-Wheels for Screw Outta/Lyon Lathes, London and New York, 1914, page' 27, states that: 6.5 inches equal 16.5 centi meters; but this equation, multiplied throughout by 2, assumes the form: 13 inches equal 33 centimeters, or 330 millimeters; as in my equation 18, above.

Norm 27 .T0 the best of my knowledge and belief, thermal expansion has not been mentioned or even referred to, either directly or indirectly, in any document that I have ever seen on the subject of change gear calculations; although its commercial importance has notbeen overlooked,'in other connections, as will appear by referring to Chisholm, 0n. the Science 0f Weighing and ill'easuring, London, 1877, page 118. Chisholm says: For all commercial purposes, on the other hand, the measure of a meter is always used at ordinary temperatures, just as a yard measure is used, and the comparig son of the two should therefore be more properly made at the same average temperature of 62 F.; that is to say, made as in my present Fig. 2.-

Scojceof the invention. NOTE 28.-If in Fig. 1 we add 5 inches of steel to bar B, and then add127 millimeters of steel to bar A, we obtain, in view of equation15, two new longer bars A and B (not shown) whose difference cl or (B-A), under the conditions of Fig. 1, is still equal to 2/10 of a millimeter. The expansion 6 of this 48-inch bar, for 30 F., is really e equal to 48/43 of d, instead of (Z; but the difference between at and e is not so great that we might not adopt, instead of equation 2,the equation, to wit; 43plus 5 or 48 inches, equal, 1092 plus 127 or 1119 millimeters. l

Norm 29.The general formula for any approximate equivalent, with constant difference (Z of 2/10 millimeter, such as defined in Note 21, evidently (43i5y) inches=(1092i127y)-1nm (28) where y' is a'whole number in the natural 1 series 0, 1, 2, 3, 4, etc. WVhen y equals zero We have equation 2, above, which is the preferred value. By making y successively equal to plus and minus 1, 2, 3, 4, 5 and 6, we obtain the 13 to 73-inch lengths llsted 1n the tabular Fig. 5. The 13-inch length is that of Lodge, or equation 18, above; while the 63-inch length is that of Boys, or equation 20, above all others are entirely novel, excepting the Chambers 438:1nch length of equation 21, which is obtained by making 1 of equation 28, equal to the excessively largefactor 79. =The W'ead equivalent, of equation 17, with d equal to zero,"1s also givenin the table for comparison with the others; and its error, for present purposes, it should be noted, is as large as 183'parts in a million.

NOTE 30.The. relative or d/M valueof 86, 129, 172 inches.

the difference d, multiplied by one million, is tabulated, in Fig. 5, under the head (LIO /M; and the corresponding departure, from the preferred value of 183 millionths, is tabulated in the same Fig. 5, under the head Error. The departures of the older solutions are seen to be: plus 4123, in the Lodge solution; minus 58, in the Boys solution; minus 165, in the Chambers solution; and minus 183, in the VVead solution. The smallest of these prior accidental departures is the departure of 58 millionths in the Boys solution; and it is plain, that any solution involving a departure smaller than 58 millionths, comes within the scope of my invention. That is to say, in the present tabular Fig. 5 the solutions yieldedby the 33, 38, -l8, 53, and 58-inch lengths are all closer to my preferred 43-inch solution than any other so far proposed by any other investigator.

No'rn 31.-Double the lengths of the bars A and B, in Fig. 1, and their difference (Z is doubled in absolute value, but without producing any change in its relative cZ/M value, or in the numerical I/M ratio, or, therefore, in the final result. If, after doubling, the 5-inch and 127 millimeters additions of Notes 21, 22 and Equation 28, above, be made, a twofold denser table of values is obtained than that given in Fig. 5. Similarly, by using any multiplier m to produce basic lengths of Am millimeters and Ba" inches, where m is a whole number taken in the series 1,2,3,4,5, etc., an endless series -of gradually denser tables may be formed,

each similar to the table of Fig. 5 and having, within the same error limits, an 00-fold, o1 gradually increasing, number of terms; and any solution in these various tables is derivable from the three general equations I: (t3wi5y) inches (29) M=(1092a2i127y) millimeters (30) d: 0.2a: millimeters (31) for, if 00, in these Equations 29, 30, and. 31, be made equal to zero, an interesting series is obtained that'includes my form of the lVead solution given in the tabular Fig. 5.

NOTE 32.-Al1 equivalents may, therefore, be tabulated, to as high a value as desired, by the mechanical method indicated in Fig. 6; which shows the result of making 00 in Equations 29, 30 and 31 successively equal to the numbers 1, 2, 3 and at; and 'y successively equal to I 0, i1, i2, :3, etc. The four basic lengths of Fig. 6 are, therefore, 43,

The VVead series, referred to in Note 32, is intentionally omitted in Fig. 6.

No'rE 33.In this Fig. 6 all solutions that are in alinement with the pole H are exact equivalents having the same I/M ratio and the same error. Thus the series 53, 106, 159, 212, etc., has an error of minus 35 parts in a million; and the series 101, 102, etc., has an error of minus 27 parts in a million. Hence all numbers that follow the smallest, in a given radially alined series, should be canceled, as not yieldingany different solution.

NOTE 34L-All solutions surrounded, in Fig. 6, by a heavy circle have an error that is either equal to, or greater than, 58 parts in a million and. can in no case be better than the solution afforded by the Boys 63- tooth Wheel. But, all solutions having an error smaller than 58 millionths, if not duplicates under Note 33, may be retained, provided the lowest prime factor involved in their use is not too large.

NOTE 35. Excluding, therefore, in Fig. 6, first, all duplicates; secondly, all results that do not comprise a prime factor higher than 199, because even a 199-tooth wheel would be inconvenientlylarge, the I values listed in the comparatively limited. chart of Fig. 6, yield fifteen different low factor equivalents, which are tabulated in Fig. 7, in order of their numerical I/M ratio, which is largest for the first, or 137-inch length;,and smallest for the last or 2417-inch length.

NOTE 36.Although Ishould not care to use most of the change gear formulae occurring between the 13 and the 33-inch lengths ofFig. 5, I am making a claim sufiiciently general to include such formulae, as I amthe first to disclose them. In this generic claim all of the different change gear formulae referred to in the present specification are more easily distinguished by their numerical I/M ratio, whose upper unattainable limit in the claim is that of Lodge and whose lower unattainable limit in the claim is that of Boys, or in decimals Lodge I/M ratio of 1a 3s0;0.o39a93e (a2) Boys I/M ratio r 63/1600:0.0393750-(33) where each of the. decimals can be completely expressed, as seen, in the form of a short period circulate.

NOTE 37.-In view of Equation 16, the,

product of I inches by 25. 1, mustequal the number of millimeters in the sum (M-i-(Z) of the tabular Fig.5; and, therefore, the I/M ratio of Note 36, multiplied by the same number 25.4 must yield the (M-l-cl) /M ratio of the same Fig. 5. The fifteen different values tabulated in the (M+(Z)/ M column of Fig. 5 may, therefore, be considered as representing the relative values of the fifteen corresponding I/M ratios, with the WVead I/M ratio-of 5/127 considered equal to unity because 5/127 multiplied by 25.4 is 127/127.

NOTE 38.--\Vhere I inches are considered equal to M millimeters, the fraction I/M evidently gives the corresponding value of one millimeter in inches, and this value multiplied by one thousand must give .the' correspondingly assumed value of the meter, in inches. That is to say, the same I/M ratio of Note 36 multiplied by 1000, or 1000-I/M, gives the number of inches in a metric screw one meter long, where .inch stands for the particularinch determined by the a pitch turns of the lead-screw that is used in cutting the metric screw.

NoTn39.-I am aware that DeVries in The Calculation of Uhcmge Wheels for Sore w Cutting on Lathes, London and New York, 19l4, page49 (copy in the U. S. Patent Ofiice Library), gives aninvolved problem which ma be restated in simple form as follows: Cut athread of pitch 3) equal to 43/56 inch, from a lead-screwcwhose pitch P is 1/2 or 28/56 inch, so 311353115 ratio of p to P is as 43 to 28.. The prob lem, however, was apparently contrived to bring in an unusual prime number, such .as 43 so as to enable the author to remark: No wheel with 43 teeth is to be found. The number 43, moreover, considered in De Vries independently of my present disclosures, has no relation whatever to metric measures; for, where De Vries does expressly refer to the. cutting of metric threads, on this same page 49, and the preceding page 48, be used the old legal or Kater value of the inch 100 cm./39.37079:2.539954 cm.)

to derive fourteen different approximate common fraction centimeter values of the inch as follows: 28/11, 94/377, 61/24, 33/13, 127 50,1019 113, 2225 376, 1 0 63, 237 113, 414/163, 511 213, 663 263, 795 313, 922/363,

.and not one of the twenty-eight different I 25. 4 Error in Inchm I milh- =M+d. nul- Inches meters M lionths.

Lodge.. 33/13 330.2: 330+0.2 1.000,606 423 Boys... 160/63 63: 1600. 2 1600+0.2 1.000,125 58 287/113 113: 2870.2: 2870+0 2 1. 000,079 104 414/163 163: 4140.2: 4140+0 2 1. 000,048 135 541/213 213: 5410.2: 5410+O.2 1. 000,037 146 668/263 263: 6680.2: 6680+0.2 1.000,030 153 795/313 313: 7950.2: 7950+0.2 1. 000,025 158 922/363 363: 9220.2: 9220+0.2 1000,022 161 1049/413 413:10490.2:10490+0.2 1.000,019 164 Chamhers 2225/876 438=11125.2=11125+0.2 1. 000,018 165 Weed... 127/50 127.0: 127+0.0 1.000,000 183 94/37 939.8: 940-02 0. 999, 787 396 61/24 12: 304.8: 305-02 0999,844 8'39 28/11 11: 279. 4: 280-06 0997,85! 2326 lower unattainable limit.

NOTE 41.The table of Note 40 shows: first, that the four De Vries fractions, to wit, 33 13, 160 63, 2225/876, and 127 50 are respectively identical with the Lodge, Boys, Chambers, and Wead solutions noted in my Fig. 5; secondly, that De Vries does not give any value lying between the Lodge solution which is my upper unattainable limit, and the Boys solution, which is my NOTE 42.The exact value of the coefficient of expansion, corresponding to the rate of conversion used in Fig. 8, being 3/50 of (Z/M or 0.06 0.2/1092 equals 0000010989; that is to say, 11 parts per million.

I claim: l r

1. The method of cutting screw threads having a pitch of 10 millimeters by means of a lathe whose lead-screw has a pitch P equal to l/n inch (n being the number of turns per inch), said method consisting in connecting the said lead-screw with the live spindle of the lathe by a train of change wheels in which the product (100, etc, of the tooth numbers in the series of driver wheels. is to the product abc, etc., of the tooth numbers in the series of driven wheels, as the product 437011, is to 1092, where the largest prime number involved is 43, necessitating the use of a driver wheel whose tooth number is 43 or a higher integral multiple of 43, such as 86 or 129.

2. The method of cutting screw threads having a pitch of 3? millimeters by means of a lathe whose lead-screw has a pitch P equal to l/n inch (n being the number of turns per inch), said method consisting in: connecting the said lead-screw with the live spindle of the lathe by a train of change wheels in which the product a 50, etc., of the tooth numbers in the series of driver wheels is to the product abo', etc., of the tooth numbers in the series of driven wheels, as the product 437m is to 1092. where the largest prime number involved is 43, necessitating the use of a driver wheel whose tooth number is 43 Or a higher integral multiple of 43. such as 86 or 129; said series of driven wheels comprising one wheel whole tooth number is equal to the product of the prime factors 7 and 13, that is to say, equal to 91.

3. The method of cutting screw threads having a-pitch of p millimeters by means of a lathe whose lead-screw has a pitch P equal to l/n inch (01. being the number of turns per inch), said method consisting in: connecting the said lead-screw with the live spindle of the lathe by a train of change wheels in which the product abs, etc, of the tooth numbers in the series of driver wheels is to the product ab'c, etc, of the tooth numbers in the series of driven wheels, as the product 12947, is to M, where I and M. re-

spectively representing inches and millimeters, are any tWo Whole numbers such that I 25.4=M 1+% c the coeflicient 0 being substantially equal to the thermal coefficient of expansion of iron in its various commercial forms, say equal to any value that is greater than eleven minus three or eight millionths, and smaller than eleven plus three or fourteen millionths.

4. The method of cutting screw threads having a pitch of 19 millimeters by means of a lathe Whose lead-screw has a pitch P equal to 1/01 inch (12, being the number of turns per inch), said method consisting in: connecting the said-lead-scre\v with the live spindle of the lathe by a train of change Wheels in Which the product abc, etc., of the tooth numbers in the series of driver Wheels is to the product abc, etc., of the tooth numbers in the series of driven Wheels, as the product 12m is to M, Where I and M,

respectively representing inches and millimeters, are any two Whole numbers such that their numerical I/M ratio shall be smaller than 13/330 and larger than 63/ 1600.

5. The method of cutting screw threads having a pitch of 39 millimeters by means of a lathe Whose lead-screw has a pitch P equal to 1/41 inch (n being the number of turns per inch), said method consisting in: con necting the said lead-screw With the live spindle of the lathe by a train of change Wheels in Which the product a120, etc., of the tooth numbers in the series of driver Wheels is to theproduct abc, etc., of the tooth numbers in the series of driven Wheels, as the product 12m is to M; Where the ratio oif-IX2'5A to M, or its equivalent (M+cZ)/M,.

is smaller than 1000,183 plus 0.000,058, or smaller than 1.000241; and is larger than 1.000,183 minus (1000,058, or larger than 1.000,125.

In testimony whereof I have signed my name to this specification.

JOSEPH BECKER.

Jopies of this patent may be obtained for five cents each, by addressing the (Commissioner of Patents,

Washington, D. G. I 

